A Does the MWI require "creation" of multiple worlds?

[Derek P]

No. Why should they be? There is only one Hamiltonian, that for the whole universe, and there is no reason at all why this Hamiltonian should have separable eigenstates. Almost no Hamiltonians, except very simple contrived ones, have this property.

Sure. Even Zurek has said that MWI may need to postulate that "there are systems". The model of detection begins with a microscopic interaction that is then amplified and decohered. If the universe can't be modeled this way then pretty well all of science falls apart.

 

[A. Neumaier]

Sure. Even Zurek has said that MWI may need to postulate that "there are systems". The model of detection begins with a microscopic interaction that is then amplified and decohered. If the universe can't be modeled this way then pretty well all of science falls apart.

Why does ''there are systems'' (or what you state about decoherence) imply that the total Hamiltonian has separable eigenstates? It doesn't. Only the initial state may be assumed (by preparation) to be separable. Apart from that, system, detector and environment are represented as terms in the total Hamiltonian, but the existence of interaction terms makes it very unlikely that the eigenstates of the total Hamiltonian are separable.

You are far too vague for a serious discussion. You neither define your terms nor point to sources where they are clearly defined.

 

[PeterDonis]

the eigenstates 1 and 2 are not eigenstates of the interacting Hamiltonian

In the model I was describing, the Hamiltonian is time-dependent; the interaction term is only "turned on" for a short period (while the particle is inside the apparatus). Before and after that, there is no interaction term in the Hamiltonian, so the kets I wrote down should be eigenstates during those times.

This is similar, as I understand it, to the way scattering experiments are modeled. Are you saying that this can only be an approximation (similar to the way you have to take the times to minus or plus infinity, heuristically speaking, to get definite "in" and "out" states in scattering--at any finite time there is still a nonzero interaction)?

 

[Derek P]

Why does ''there are systems'' (or what you state about decoherence) imply that the total Hamiltonian has separable eigenstates? It doesn't. Only the initial state may be assumed (by preparation) to be separable. Apart from that, system, detector and environment are represented as terms in the total Hamiltonian, but the existence of interaction terms makes it very unlikely that the eigenstates of the total Hamiltonian are separable.

You are far too vague for a serious discussion. You neither define your terms nor point to sources where they are clearly defined.

Yeah, you're probably right. Ta-ta!

 

[A. Neumaier]

the interaction term is only "turned on" for a short period (while the particle is inside the apparatus). Before and after that, there is no interaction term in the Hamiltonian, so the kets I wrote down should be eigenstates during those times.

This still doesn't change my analysis; it just restricts it to the short period where the interaction is on. Afterwards the system is stationary so nothing changes.

This is similar, as I understand it, to the way scattering experiments are modeled. Are you saying that this can only be an approximation (similar to the way you have to take the times to minus or plus infinity, heuristically speaking, to get definite "in" and "out" states in scattering--at any finite time there is still a nonzero interaction)?

Indeed, it is only an approximation. But even when the interaction time is taken to be finite, the analysis still leads to the same strange result. Separability is lost once the interaction is turned on, hence (in microscopic terms) long before the measurement is completed. Thus with your revised definition, the worlds split at the moment the measurement begins, and the result in each world is predetermined.

Moreover, if one thinks of reversing the situation (unitary dynamics is reversible), worlds should disappear (merge) whenever two states of the detector happen to become equal. This is quite unreasonable from a formal point of view. The natural thing to expect is that the two worlds were always there, and will always be there, which is the reversible situation. The other, even more natural interpretation is that the worlds are an artifact of imposing a particular tensor product basis on the universe, and appear and disappear together with the coordinate system. This is what I had in mind when asking about the ''point of view'' interpretation.

Note also that nothing is said by this version of the MWI about how the worlds are selected by a real observer - they all have fully democratic existence of the same kind. Labeling them by a formal number called probability is of course possible, but nothing explains why this formal label actually has the property of an observed relative frequency by an observer moving along a particular (coarse-grained) world line.

 

[PeterDonis]

The natural thing to expect is that the two worlds were always there, and will always be there, which is the reversible situation. The other, even more natural interpretation is that the worlds are an artifact of imposing a particular tensor product basis on the universe, and appear and disappear together with the coordinate system.

For purposes of this discussion, given its title question, I think both of these alternatives support the answer "no"; the MWI does not create worlds.

 

[A. Neumaier]

For purposes of this discussion, given its title question, I think both of these alternatives support the answer "no"; the MWI does not create worlds.

With the meaning of the terms implied by our discussion, this is a fair conclusion.

 

[Mentz114]

With the meaning of the terms implied by our discussion, this is a fair conclusion.

Thank you for your contribution to this thread. Also @PeterDonis and others.
Even for someone acutely sceptical about MWI it has been instructive (and entertaining).

 

[romsofia]

Sure. Even Zurek has said that MWI may need to postulate that "there are systems".

That is a postulate of MWI.

"Everett, Wheeler and Graham (EWG) postulate that the real world, or any isolated part of it one may wish for the moment to regard as the world, is faithfully represented solely by the following mathematical objects: a vector in a Hilbert space; a set of dynamical equations (derived from a variational principle) for a set of operators that act on the Hilbert space, and a set of commutation relations for the operators (derived from the Poisson brackets of the classical theory by the quantization rule, where classical analogs exist). Only one additional postulate is then needed to give physical meaning to the mathematics. This is the postulate of complexity: The world must be sufficiently complicated that it be decomposable into systems and apparatuses."

As far as I am aware, you need branches (worlds) for MWI to work. That's just how it is set up. To me though, MWI is just a causal interpretation of QM.

I'm not going to attempt to make points in regards to MWI better than Bryce DeWitt, so start with the article I linked in post 95, but here is a more readable version: http://cqi.inf.usi.ch/qic/deWitt1970.pdf I will address issues with regards to this, but I can't be bothered going through this whole thread as I joined the discussion too late.

If you can't find his paper "The Everett-Wheeler Interpretation of Quantum Mechanics," I can try and get a photo copy of it from my library in the next few days.

 

[PeterDonis]

I can try and get a photo copy of it from my library in the next few days.

Unfortunately we can't post scans of library copies here, due to copyright issues. Many older papers are available online now.

 

[Derek P]

That is a postulate of MWI.
Only one additional postulate is then needed to give physical meaning to the mathematics. This is the postulate of complexity: The world must be sufficiently complicated that it be decomposable into systems and apparatuses."

I think Zurek's point was a bit different from that but it doesn't matter now as I'm "far too vague for a serious discussion."

As far as I am aware, you need branches (worlds) for MWI to work.

They exist in the maths, which is postulated to be ontic. You don't need to postulate them twice.

 

[stevendaryl]

Why does ''there are systems'' (or what you state about decoherence) imply that the total Hamiltonian has separable eigenstates?

What does "separable eigenstates" mean here? Are you talking about being able to write the total wave function as a product?

 

[stevendaryl]

Surely they are eigenstates of the total interaction including interaction with the "environment"? The states are already superposed and therefore evolving independently before decoherence starts. Or maybe I'm just not getting the point.

It wasn't clear at all to me what the exchange between you and @A. Neumaier about "separable solutions" meant.

What I think is at issue is whether you can write a state of the universe as a product state: $|\psi\rangle = |\psi_A\rangle |\phi_B\rangle$ where $|\psi_A\rangle$ is the state of some object, $A$, and $|\phi_B\rangle$ is the state of some other object, $B$. If the two objects are macroscopic, then you probably can't maintain such a product representation. The two objects will quickly become entangled.

 

[Derek P]

It wasn't clear at all to me what the exchange between you and @A. Neumaier about "separable solutions" meant.

Well it's not very clear to me either.

What I think is at issue is whether you can write a state of the universe as a product state: $|\psi\rangle = |\psi_A\rangle |\phi_B\rangle$ where $|\psi_A\rangle$ is the state of some object, $A$, and $|\phi_B\rangle$ is the state of some other object, $B$. If the two objects are macroscopic, then you probably can't maintain such a product representation. The two objects will quickly become entangled.

Yes. That's what we want isn't it?
But frankly I'm tired of this discussion. Either you can write the state as a sum of products using THREE kets each and allow the second two to interact later, or you can't. If you can't then MWI and most of measurement theory is junk. But I can't for the life of me see why you shouldn't.

 

[A. Neumaier]

What does "separable eigenstates" mean here? Are you talking about being able to write the total wave function as a product?

It wasn't clear at all to me what the exchange between you and @A. Neumaier about "separable solutions" meant.

What I think is at issue is whether you can write a state of the universe as a product state: $|\psi\rangle = |\psi_A\rangle |\phi_B\rangle$ where $|\psi_A\rangle$ is the state of some object, $A$, and $|\phi_B\rangle$ is the state of some other object, $B$. If the two objects are macroscopic, then you probably can't maintain such a product representation. The two objects will quickly become entangled.

Separable state = product state.

 

[ronronron3]

My impression has been that the 'many-worlds' interpretation is, at present, at best a metaphor based on an analogy with unix processes as below. Just the sort of thing that might turn out to be true or at least illuminating of course.

From http://www.csl.mtu.edu/cs4411.ck/www/NOTES/process/fork/create.html

"System call fork() is used to create processes. It takes no arguments and returns a process ID. The purpose of fork() is to create a new process, which becomes the child process of the caller. After a new child process is created, both processes will execute the next instruction following the fork() system call. Therefore, we have to distinguish the parent from the child. This can be done by testing the returned value of fork():

• If fork() returns a negative value, the creation of a child process was unsuccessful.
• fork() returns a zero to the newly created child process.
• fork() returns a positive value, the process ID of the child process, to the parent. The returned process ID is of type pid_t defined in sys/types.h. Normally, the process ID is an integer. Moreover, a process can use function getpid() to retrieve the process ID assigned to this process.

Therefore, after the system call to fork(), a simple test can tell which process is the child. Please note that Unix will make an exact copy of the parent's address space and give it to the child. Therefore, the parent and child processes have separate address spaces."

 

[Mentz114]

My impression has been that the 'many-worlds' interpretation is, at present, at best a metaphor based on an analogy with unix processes as below. Just the sort of thing that might turn out to be true or at least illuminating of course.

From http://www.csl.mtu.edu/cs4411.ck/www/NOTES/process/fork/create.html

"System call fork() is used to create processes. It takes no arguments and returns a process ID. The purpose of fork() is to create a new process, which becomes the child process of the caller. After a new child process is created, both processes will execute the next instruction following the fork() system call. Therefore, we have to distinguish the parent from the child. This can be done by testing the returned value of fork():

• If fork() returns a negative value, the creation of a child process was unsuccessful.
• fork() returns a zero to the newly created child process.
• fork() returns a positive value, the process ID of the child process, to the parent. The returned process ID is of type pid_t defined in sys/types.h. Normally, the process ID is an integer. Moreover, a process can use function getpid() to retrieve the process ID assigned to this process.

Therefore, after the system call to fork(), a simple test can tell which process is the child. Please note that Unix will make an exact copy of the parent's address space and give it to the child. Therefore, the parent and child processes have separate address spaces."

I think this is off-topic but the anaology does not hold because the wave function of the universe does not contain enough to make the split. Therefore an outside agency is required, which contradicts the postulate that the WF is all that exists.

 

[PeterDonis]

the wave function of the universe does not contain enough to make the split

Why not?

 

[Mentz114]

Why not?

In what little I've read about MWI this has not been made explicit. I can't find anything that could correspond to a creation operator for a universe in the standard formalism.

 

[PeterDonis]

I can't find anything that could correspond to a creation operator for a universe in the standard formalism.

There isn't one. The total quantum state of the universe in the MWI is just a pure state that evolves by unitary evolution. You can't create or annihilate it.

 

[Derek P]

I think this is off-topic but the anaology does not hold because the wave function of the universe does not contain enough to make the split. Therefore an outside agency is required, which contradicts the postulate that the WF is all that exists.

No, the split is the decoherence of some subsystems as a result of interaction with others.

 

[Derek P]

In what little I've read about MWI this has not been made explicit. I can't find anything that could correspond to a creation operator for a universe in the standard formalism.

I think you may be confusing worlds with universes. Unless you're harking back to the OP and simply saying "no it does not" :)

 

[Mentz114]

There isn't one. The total quantum state of the universe in the MWI is just a pure state that evolves by unitary evolution. You can't create or annihilate it.

Where does 'copying' or 'splitting' come in ?
I have to admit that I don't know ( or I cannot accept) what you are saying.

No, the split is the decoherence of some subsystems as a result of interaction with others.

At which time t a copy is made ?

I think you may be confusing worlds with universes. Unless you're harking back to the OP and simply saying "no it does not" :)

Are the 'worlds' contained in 'universes' ?

Of course, the computing analogy breaks down because it requires a computer to do the eveolution and splitting.
Is the Hamiltonian the 'computer' ? Since it is required to perform the evolution.

 

[PeterDonis]

Where does 'copying' or 'splitting' come in ?

There is no copying. "Splitting", as I think @A. Neumaier clarified very well in his subthread with me, is not really well defined by MWI proponents, but basically it amounts to picking a basis that reflects the eigenstates of the measuring apparatus, and calling each term in a superposition of product states of the measured system and measuring apparatus eigenstates in that basis a "world". My OP to this thread described such a state; the $|U>$ and $|D>$ kets in that state describe eigenstates of the measuring apparatus, and the final state described therefore has two "worlds" in it. Then an interaction that takes a state like the initial state in my OP, which is separable, into an entangled superposition of multiple "worlds" as just defined, is what is meant in the MWI by "splitting" into multiple worlds.

 

[Mentz114]

There is no copying. "Splitting", as I think @A. Neumaier clarified very well in his subthread with me, is not really well defined by MWI proponents, but basically it amounts to picking a basis that reflects the eigenstates of the measuring apparatus, and calling each term in a superposition of product states of the measured system and measuring apparatus eigenstates in that basis a "world". My OP to this thread described such a state; the $|U>$ and $|D>$ kets in that state describe eigenstates of the measuring apparatus, and the final state described therefore has two "worlds" in it. Then an interaction that takes a state like the initial state in my OP, which is separable, into an entangled superposition of multiple "worlds" as just defined, is what is meant in the MWI by "splitting" into multiple worlds.

Can what you are saying be expressed mathematically ? I really can't see where the splits come from or end up.
Until there are equations in which all the 'splits' are explicit surely MWI is just handwaving.

A superposition of observable states is already splittable. But it's only meaningful to call them worlds when their interaction with the detector and the environment has created a superposition of global states each of which is consistent with one of the observed outcomes i.e. an improper mixture.

The physics of MWI is just unitary QM.

The usual postulate of QM says that we will get an eigenfunction $m$ of the operator with probability $|\alpha_m|^2$. There is nothing about splitting.
I presume that the wave function of the universe $\psi_\Omega$ must satisfy something like $\hat{H}_\Omega \psi_\Omega = C\psi_\Omega$ where $C$ is a constant. There two things in that equation.

Thanks for the responses.

 

[stevendaryl]

Can what you are saying be expressed mathematically ? I really can't see where the splits come from or end up.

That's because there are no splits. What is sometimes picturesquely described as the world splitting is that if the universe is initially in a state in which a macroscopic property has a definite value, then interactions will lead to a state in which it does not have a definite value.

We can make this concrete by fine-graining. Let's pick some partitioning of the universe into little cubes of size maybe 1 cubic millimeter. Pick some indexing scheme so that each cube is defined by three integer indices $i, j, k$. Then we can define a set of observables:

$\vec{E}_{ijk}$ = the average electric field in cube number $i,j,k$
$\vec{B}_{ijk}$ = the average magnetic field in that cube.
$U_{ijk}$ = the total energy within the cube.
$Q_{ijk}$ = the total charge within the cube.

So we can (I assume) describe the Hilbert space of the universe using a basis of eigenstates of our countably many operators (they will approximately commute). (In general, there will be many eigenstates with the same values for those 4 operators).

So the phenomenon that might be described as "splitting" is that in certain circumstances, an eigenstate of our macroscopic operators may evolve into a state that is a superposition of different values for those macroscopic operators.

 

[PeterDonis]

Can what you are saying be expressed mathematically ?

Have you looked at the OP of this thread?

 

[PeterDonis]

I presume that the wave function of the universe $\psi_\Omega$ must satisfy something like $\hat{H}_\Omega \psi_\Omega = C\psi_\Omega$ where $C$ is a constant.

That is saying that the wave function of the universe must be an eigenstate of the universal Hamiltonian. Why would that have to be the case?

 

[Mentz114]

Have you looked at the OP of this thread?

Will do so again.

That is saying that the wave function of the universe must be an eigenstate of the universal Hamiltonian. Why would that have to be the case?

I did qualify this with 'something like'.

The point is, does $\hat{H}_\Omega$ have an independent existence from $\psi_\Omega$ ?

 

[Mentz114]

That's because there are no splits. What is sometimes picturesquely described as the world splitting is that if the universe is initially in a state in which a macroscopic property has a definite value, then interactions will lead to a state in which it does not have a definite value.
[..]
So the phenomenon that might be described as "splitting" is that in certain circumstances, an eigenstate of our macroscopic operators may evolve into a state that is a superposition of different values for those macroscopic operators.

Cute reply. I will take a while to absorb this and maybe write equations.

 

[PeterDonis]

does $\hat{H}_\Omega$ have an independent existence from $\psi_\Omega$ ?

$\psi$ is the state and $\hat{H}$ governs its dynamical evolution in time. I'm not sure whether that makes the answer to this "yes" or "no".

 

[Stephen Tashi]

The common interpretation of a probabilistic situation is that there are several "possible" outcomes and only one of them "actually' occurs. In the MWI (and other interpretations of QM that do not allow collapse of wave functions) is such an interpretation possible?

If so, what kind of events are the "possible" outcomes - of which only one "actually" occurs?

If not, then what is the physical interpretation of probability?

 

[PeterDonis]

In the MWI (and other interpretations of QM that do not allow collapse of wave functions) is such an interpretation possible?

No; the interpretation explicitly says that all of the outcomes occur. (More precisely, it says that unitary evolution is always valid, which obviously implies that all outcomes occur.)

If not, then what is the physical interpretation of probability?

As I understand it this is one of the key unresolved issues with the MWI.

 

[Mentz114]

$\psi$ is the state and $\hat{H}$ governs its dynamical evolution in time. I'm not sure whether that makes the answer to this "yes" or "no".

I don't know either.

if $\hat{H}_\Omega=|\psi_\Omega\rangle \langle \psi_\Omega|$ then $\hat{H}_\Omega\psi_\Omega=\psi_\Omega$ and $\hat{H}_\Omega$ depends on the basis selected for $\psi_\Omega$. Is that right ? In which case they are not independent.

 

[PeterDonis]

if $\hat{H}_\Omega=|\psi_\Omega\rangle \langle \psi_\Omega|$ then $\hat{H}_\Omega\psi_\Omega=\psi_\Omega$

Yes. In this special case, the universal wave function would be constant in time (since it is an eigenstate of the Hamiltonian). But there is nothing that requires this to be the case.

and $\hat{H}_\Omega$ depends on the basis selected for $\psi_\Omega$. Is that right ?

No. The equation $\hat{H}_\Omega=|\psi_\Omega\rangle \langle \psi_\Omega|$ is basis independent. Equivalently, whether a particular state vector is an eigenvector of a particular operator is basis independent.

 

[Mentz114]

Yes. In this special case, the universal wave function would be constant in time (since it is an eigenstate of the Hamiltonian). But there is nothing that requires this to be the case.

So the universal wave function may depend on time ? And
$\hat{H}_\Omega(t,x)=|\psi_\Omega\rangle \langle \psi_\Omega|$

No. The equation $\hat{H}_\Omega=|\psi_\Omega\rangle \langle \psi_\Omega|$ is basis independent. Equivalently, whether a particular state vector is an eigenvector of a particular operator is basis independent.

OK, thanks.

I still can't work out if the Hamiltonian and the wave function contain exactly the same information.

 

[PeterDonis]

So the universal wave function may depend on time ?

I don't see what would rule out such a model.

And
$\hat{H}_\Omega(t,x)=|\psi_\Omega\rangle \langle \psi_\Omega|$

No. If $|\psi_\Omega\rangle$ depends on time, then it's not an eigenstate of $\hat{H}_\Omega$, which means $\hat{H}_\Omega \neq |\psi_\Omega\rangle \langle \psi_\Omega|$.

Having $\hat{H}$ itself depend on time is something different.

 

[PeterDonis]

I still can't work out if the Hamiltonian and the wave function contain exactly the same information.

One is a state and the other is the operator you apply to states to see how they evolve in time. To me that means they don't contain the same information.

 

[Mentz114]

I don't see what would rule out such a model.

I could be wrong but is the universe not considered to be a closed system in MWI and so it cannot gain or lose energy.
I ought to look this up.

No. If $|\psi_\Omega\rangle$ depends on time, then it's not an eigenstate of $\hat{H}_\Omega$, which means $\hat{H}_\Omega \neq |\psi_\Omega\rangle \langle \psi_\Omega|$.

Having $\hat{H}$ itself depend on time is something different.

Yes, sorry I'm a bit rusty but its coming back ...

One is a state and the other is the operator you apply to states to see how they evolve in time. To me that means they don't contain the same information.

OK, I'll think about that.

 

[kith]

If not, then what is the physical interpretation of probability?

There have been attempts to use a decision theoretic approach, i.e. probabilities are related to how a rational agent would need to act in order to maximize his utility. The current state of affairs seems to be the 2009 paper "A formal proof of the Born rule from decision-theoretic assumptions" by David Wallace.

 

[PeterDonis]

is the universe not considered to be a closed system in MWI

Yes, in the sense that it's in a pure state.

and so it cannot gain or lose energy

It's quite possible that MWI proponents assume that. I don't know if it's actually required for consistency of the model.

 

[Mentz114]

Yes, in the sense that it's in a pure state.
[..]
It's quite possible that MWI proponents assume that. I don't know if it's actually required for consistency of the model.

Thanks, Peter. My ignorance about MWI is showing.

About the independence of the Hamiltonian and universal WF - it seems the Hamiltonian must have the whole future of the UWF encoded in it.

I have to log off for a while now.

 

[A. Neumaier]

the split is the decoherence of some subsystems as a result of interaction with others.

This is very vague and probably meaningless. Decoherence is a continuous process that happens to the density operator, while a split is by its nature something instantaneous.

That's because there are no splits. What is sometimes picturesquely described as the world splitting is that if the universe is initially in a state in which a macroscopic property has a definite value, then interactions will lead to a state in which it does not have a definite value.

Yes. And this happens whenever there are interactions. Thus the unsplit world exists only for a moment of infinitesimal length.

the interpretation explicitly says that all of the outcomes occur.

Does it? The interpretation explicitly says that there are worlds for each possible outcome. But since a world is not ''the universe'', and ''outcome'' is never defined, it doesn't really say anything about outcomes. The latter should be what comes actually out, which is a single result.

I presume that the wave function of the universe $\psi_\Omega$ must satisfy something like $\hat{H}_\Omega \psi_\Omega = C\psi_\Omega$ where $C$ is a constant.

This is certainly wrong, as it would mean that the wave function doesn't evolve in time.

if the Hamiltonian and the wave function contain exactly the same information.

No. The wave function contains the information about the state at a particular time, and the Hamiltonian tells how it changes with time.

is the universe not considered to be a closed system in MWI

This only implies that the expectation value of the Hamiltonian is constant.

it seems the Hamiltonian must have the whole future of the UWF encoded in it.

The Hamiltonian provides the evolution equation, and the wave function at a fixed time provides the initial condition. Both are needed to fix the future of the wave function.

 

[Derek P]

This is very vague and probably meaningless.

Yeah, strange how I keep coming up with vague and meaningless statements.

Decoherence is a continuous process that happens to the density operator

Correct.

a split is by its nature something instantaneous.

If you assume that then you will find yourself having a long tedious and unproductive argument on PhysicsForums trying to pin down the exact moment that the split occurs. Good luck with that.

 

[A. Neumaier]

If you assume that then you will find yourself having a long tedious and unproductive argument on PhysicsForums trying to pin down the exact moment that the split occurs. Good luck with that.

Please tell me how something can split without a discrete moment where the split happens. If you split a plank into two there is a moment where the plank gets disconnected, i.e., is split. The discreteness is in the notion itself, independent of the application.

But apparently nothing ever splits in MWI, and ''split'', like ''world'', is a misnomer.

 

[Derek P]

Please tell me how something can split without a discrete moment where the split happens. If you split a plank into two there is a moment where the plank gets disconnected, i.e., is split. The discreteness is in the notion itself, independent of the application.

Yes, I have come across the phenomenon of splitting planks. Also of splitting hairs. Last time I looked it was a continuous process of fibre rupture and then separation of molecules held together by Van de Waals forces. So no exact moment. It's the same with worlds splitting. It is a continuous process quite easily described as the diagonalization of the density matrix through decoherence. So it can be quantified, leaving it as a function of time which is asymptotically zero in time past and asymptotically100% in time future. The only remaining arbitrariness is deciding what level of diagonalization is "complete for all practical purposes".

But apparently nothing ever splits in MWI, and ''split'', like ''world'', is a misnomer.

Then you have been misinformed.

 

[lukesfn]

I've been curious about a similar question to the OP which this thread has been circling around.

I'm quite ignorant compared to most posters here though so please forgive imprecise use of words.

(btw, because I always hear comments worlds splitting in MWI, it leads me to believe the worlds in MWI as usually referred to, must be distinguishable worlds. Alternatively you could imagine many extra indistinguishable worlds that rather then spit, become distinguishable. Probabilities may be more intuitive interpreting this way)

Anyway, my question is that if the universe is in equilibrium, then wouldn't we think that MWI doesn't even lead to an increase in distinguishable worlds? Worlds would merge at the same rate the spit?

Similar to the OP, I see a lot of people making prediction of infinite future increase in worlds in MWI, but it would seem not necessarily so.

 

[johnkclark]

The key is what "collapse of the wave function" means physically, I think it means there is something special about one particular state of that function. The Many World's Interpretation says no state is special, nothing collapses, and everything that can happen does happen. This is how I think the MWI would describe several variations of the two-slit experiment:

In the usual experiment the universe splits when it passes the two slits because the 2 worlds are different, but when the photons hit the film and they no longer exist in either world so the 2 worlds are identical once more and the universes fuse back together again. Looking back from that fused world we find evidence that the photon went through slit X only and evidence it went through slit Y only and this causes an interference pattern. There is nothing special about an observer in this, the same thing would happen if nobody looked at the film, or even if you used a brick wall instead of film, because the important thing is not that the photon makes a record (whatever that is) but simply that it is destroyed. Mind has nothing to do with any of this so unlike the Copenhagen interpretation the MWI doesn't need to explain it, or explain what “measurement" means, or “record", or “observation", or “consciousness". That is a very very big advantage! The key point is that worlds split when they become different and merge when they become the same.

Now do the two-slit experiment again but instead of using film to stop the photon after it passes the slits, let it head out into infinite space. If Many Worlds is correct then the entire universe splits into 2 when the photon hit's the 2 slits and never recombines. There is nothing special about you the observer, you split just like everything else, you know that the photon went through one and only one slit, but of course you have no way of knowing which one.

It's more difficult to do but the 2 slit experiment can be set up in such a way that you can tell which slit the photon went through, but if you do that then the photons will not produce an interference pattern on the film. This is because even after the photon hits the film in both worlds and is destroyed the worlds remain different, in one the physical memory pattern in my brain encodes that the photon went through slot X and in the other slot Y, so the worlds don’t merge back together and no interference pattern is seen in either world.

Separate worlds only emerge if there is a difference between them, if the worlds evolve in such a way that the difference disappears then re-coherence occurs. For obvious reasons re-coherence can only occur if the 2 worlds are only very slightly different and have only been separated for a short time, and that is why experiments of this sort are difficult and it explains why in our everyday world we don’t see macro objects becoming entangled and even atoms aren’t usually entangled for long at room temperatures.

John K Clark

 

[A. Neumaier]

worlds splitting. It is a continuous process quite easily described as the diagonalization of the density matrix through decoherence. So it can be quantified, leaving it as a function of time which is asymptotically zero in time past and asymptotically100% in time future. The only remaining arbitrariness is deciding what level of diagonalization is "complete for all practical purposes".

This is the first time you provide substance to the discussion. Please add a bit of detail by telling us what in the decoherence process are the worlds, and when, "for all practical purposes", there is only one world and when there are several. Or are there from the beginning infinitely many worlds?

 

[PeterDonis]

it seems the Hamiltonian must have the whole future of the UWF encoded in it.

Since unitary evolution is deterministic, yes, knowing the state vector at any time and knowing the Hamiltonian means that you know the entire history of the state vector.